How to Calculate Condition Number

The condition number of a matrix A is defined as:

κ(A) = ||A|| × ||A⁻¹||

Where:

• ||A|| is the matrix norm of A
• ||A⁻¹|| is the matrix norm of the inverse of A

For different norm types:

• 1-norm: Maximum absolute column sum
• 2-norm: Square root of largest eigenvalue of AᵀA
• ∞-norm: Maximum absolute row sum

Interpretation:

• κ(A) ≈ 1: Well-conditioned matrix
• κ(A) >> 1: Ill-conditioned matrix